Free · Algebra and geometric models

Sides and Angles of Similar Triangles

Solve two similar triangles from SSS or included-angle SAS data and one corresponding second-triangle side.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

For the worked inputs, B = 8, C = 10.

a′/a=b′/b=c′/c; corresponding angles are equal

Worked example

Enter these known values and leave the other values blank.

Given
0
a
3 cm
b
4 cm
c
5 cm
A
6 cm
α
36.87 deg
β
53.13 deg
γ
90 deg
B
8 cm
C
10 cm

Assumptions and limitations

  • Side lengths are positive and form strict triangles.
  • Similarity uses corresponding side names and a positive common scale factor. SAS uses the included angle.

Common questions

What must I enter?

Choose the mode when available and enter its independent known quantities. Leave an unknown editable quantity empty to use a supported inverse.

How should I use the result?

Interpret the numbers within the stated mathematical assumptions. Available unit selectors convert quantities; display rounding does not replace the internal calculation.

References

Explicit real-model bounds validate dimensions, inverse branches and discrete controls omitted or approximated in this capture.

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